A random-walk/giant-loop model for interphase chromosomes

Organization and Dynamics of Chromosomes

How long thread-like eukaryotic chromosomes fit tidily in the small volume of the nucleus without significant entanglement is just beginning to be understood, thanks to major advances in experimental techniques. Several polymer models, which reproduce contact maps that measure the probabilities that two loci are in spatial contact, have predicted the 3D structures of interphase chromosomes. Data-driven approaches, using contact maps as input, predict that mitotic helical chromosomes are characterized by a switch in handedness, referred to as perversion. By using experimentally derived effective interactions between chromatin loci in simulations, structures of conventional and inverted nuclei have been accurately predicted. Polymer theory and simulations show that the dynamics of individual loci in chromatin exhibit subdiffusive behavior but the diffusion exponents are broadly distributed, which accords well with experiments. Although coarse-grained models are successful, many challenging problems remain, which require the creation of new experimental and computational tools to understand genome biology.

Bridging scales in chromatin organization: Computational models of loop formation and their implications for genome function

Chromatin loop formation plays a crucial role in 3D genome interactions, with misfolding potentially leading to irregular gene expression and various diseases. While experimental tools such as Hi-C have advanced our understanding of genome interactions, the biophysical principles underlying chromatin loop formation remain elusive. This review examines computational approaches to chromatin folding, focusing on polymer models that elucidate chromatin loop mechanics. We discuss three key models: (1) the multi-loop-subcompartment model, which investigates the structural effects of loops on chromatin conformation; (2) the strings and binders switch model, capturing thermodynamic chromatin aggregation; and (3) the loop extrusion model, revealing the role of structural maintenance of chromosome complexes. In addition, we explore advanced models that address chromatin clustering heterogeneity in biological processes and disease progression. The review concludes with an outlook on open questions and current trends in chromatin loop formation and genome interactions, emphasizing the physical and computational challenges in the field.

The chromosome folding problem and how cells solve it

Every cell must solve the problem of how to fold its genome. We describe how the folded state of chromosomes is the result of the combined activity of multiple conserved mechanisms. Homotypic affinity-driven interactions lead to spatial partitioning of active and inactive loci. Molecular motors fold chromosomes through loop extrusion. Topological features such as supercoiling and entanglements contribute to chromosome folding and its dynamics, and tethering loci to sub-nuclear structures adds additional constraints. Dramatically diverse chromosome conformations observed throughout the cell cycle and across the tree of life can be explained through differential regulation and implementation of these basic mechanisms. We propose that the first functions of chromosome folding are to mediate genome replication, compaction, and segregation and that mechanisms of folding have subsequently been co-opted for other roles, including long-range gene regulation, in different conditions, cell types, and species.

Formamide denaturation of double-stranded DNA for fluorescence in situ hybridization (FISH) distorts nanoscale chromatin structure

As imaging techniques rapidly evolve to probe nanoscale genome organization at higher resolution, it is critical to consider how the reagents and procedures involved in sample preparation affect chromatin at the relevant length scales. Here, we investigate the effects of fluorescent labeling of DNA sequences within chromatin using the gold standard technique of three-dimensional fluorescence in situ hybridization (3D FISH). The chemical reagents involved in the 3D FISH protocol, specifically formamide, cause significant alterations to the sub-200 nm (sub-Mbp) chromatin structure. Alternatively, two labeling methods that do not rely on formamide denaturation, resolution after single-strand exonuclease resection (RASER)-FISH and clustered regularly interspaced short palindromic repeats (CRISPR)-Sirius, had minimal impact on the three-dimensional organization of chromatin. We present a polymer physics-based analysis of these protocols with guidelines for their interpretation when assessing chromatin structure using currently available techniques.

Correlative single molecule lattice light sheet imaging reveals the dynamic relationship between nucleosomes and the local chromatin environment

In the nucleus, biological processes are driven by proteins that diffuse through and bind to a meshwork of nucleic acid polymers. To better understand this interplay, we present an imaging platform to simultaneously visualize single protein dynamics together with the local chromatin environment in live cells. Together with super-resolution imaging, new fluorescent probes, and biophysical modeling, we demonstrate that nucleosomes display differential diffusion and packing arrangements as chromatin density increases whereas the viscoelastic properties and accessibility of the interchromatin space remain constant. Perturbing nuclear functions impacts nucleosome diffusive properties in a manner that is dependent both on local chromatin density and on relative location within the nucleus. Our results support a model wherein transcription locally stabilizes nucleosomes while simultaneously allowing for the free exchange of nuclear proteins. Additionally, they reveal that nuclear heterogeneity arises from both active and passive processes and highlight the need to account for different organizational principles when modeling different chromatin environments.

Robustness of carbon-ion radiotherapy against DNA damage repair associated radiosensitivity variation based on a biophysical model

BACKGROUND

Interpatient variation of tumor radiosensitivity is rarely considered during the treatment planning process despite its known significance for the therapeutic outcome.

PURPOSE

To apply our mechanistic biophysical model to investigate the biological robustness of carbon ion radiotherapy (CIRT) against DNA damage repair interference (DDRi) associated patient-to-patient variability in radiosensitivity and its potential clinical advantages against conventional radiotherapy approaches.

METHODS AND MATERIALS

The "UNIfied and VERSatile bio response Engine" (UNIVERSE) was extended by carbon ions and its predictions were compared to a panel of in vitro and in vivo data including various endpoints and DDRi settings within clinically relevant dose and linear energy transfer (LET) ranges. The implications of UNIVERSE predictions were then assessed in a clinical patient scenario considering DDRi variance.

RESULTS

UNIVERSE tests well against the applied benchmarks. While in vitro survival curves were predicted with an R2 > 0.92, deviations from in vivo RBE data were less than 5.6% The conducted paradigmatic patient plan study implies a markedly reduced significance of DDRi based radiosensitivity variability in CIRT (13% change ofD 50 ${{D}_{50}}$ in target) compared to conventional radiotherapy (62%) and that boosting the LET within the target further amplifies this robustness of CIRT (8%). In the case of heightened tumor radiosensitivity, a dose de-escalation strategy for photons allows a reduction of the maximum effective dose within the normal tissue (NT) from aD 2 ${{D}_2}$ of 2.65 to 1.64 Gy, which lies below the level found for CIRT (D 2 ${{D}_2}$  = 2.41 Gy) for the analyzed plan and parameters. However, even after de-escalation, the integral effective dose in the NT is found to be substantially higher for conventional radiotherapy in comparison to CIRT (D m e a n ${{D}_{mean}}$ of 0.75, 0.46, and 0.24 Gy for the conventional plan, its de-escalation and CIRT, respectively).

CONCLUSIONS

The framework offers adequate predictions of in vitro and in vivo radiation effects of CIRT while allowing the consideration of DRRi based solely on parameters derived from photon data. The results of the patient planning study underline the potential of CIRT to minimize important sources of interpatient divergence in therapy outcome, especially when combined with techniques that allow to maximize the LET within the tumor. Despite the potential of de-escalation strategies for conventional radiotherapy to reduce the maximum effective dose in the NT, CIRT appears to remain a more favorable option due to its ability to reduce the integral effective dose within the NT.

Footprints of loop extrusion in statistics of intra-chromosomal distances: An analytically solvable model

Active loop extrusion-the process of formation of dynamically growing chromatin loops due to the motor activity of DNA-binding protein complexes-is a firmly established mechanism responsible for chromatin spatial organization at different stages of a cell cycle in eukaryotes and bacteria. The theoretical insight into the effect of loop extrusion on the experimentally measured statistics of chromatin conformation can be gained with an appropriately chosen polymer model. Here, we consider the simplest analytically solvable model of an interphase chromosome, which is treated as an ideal chain with disorder of sufficiently sparse random loops whose conformations are sampled from the equilibrium ensemble. This framework allows us to arrive at the closed-form analytical expression for the mean-squared distance between pairs of genomic loci, which is valid beyond the one-loop approximation in diagrammatic representation. In addition, we analyze the loop-induced deviation of chain conformations from the Gaussian statistics by calculating kurtosis of probability density of the pairwise separation vector. The presented results suggest the possible ways of estimating the characteristics of the loop extrusion process based on the experimental data on the scale-dependent statistics of intra-chromosomal pair-wise distances.

Human Coronavirus Infection Reorganizes Spatial Genomic Architecture in Permissive Lung Cells

Chromatin conformation capture followed by next-generation sequencing in combination with large-scale polymer simulations (4DHiC) produces detailed information on genomic loci interactions, allowing for the interrogation of 3D spatial genomic structures. Here, Hi-C data was acquired from the infection of fetal lung fibroblast (MRC5) cells with α-coronavirus 229E (CoV229E). Experimental Hi-C contact maps were used to determine viral-induced changes in genomic architecture over a 48-hour time period following viral infection, revealing substantial alterations in contacts within chromosomes and in contacts between different chromosomes. To gain further structural insight and quantify the underlying changes, we applied the 4DHiC polymer simulation method to reconstruct the 3D genomic structures and dynamics corresponding to the Hi-C maps. The models successfully reproduced experimental Hi-C data, including the changes in contacts induced by viral infection. Our 3D spatial simulations uncovered widespread chromatin restructuring, including increased chromosome compactness and A-B compartment mixing arising from infection. Our model also suggests increased spatial accessibility to regions containing interferon-stimulated genes upon infection with CoV229E, followed by chromatin restructuring at later time points, potentially inducing the migration of chromatin into more compact regions. This is consistent with previously observed suppression of gene expression. Our spatial genomics study provides a mechanistic structural basis for changes in chromosome architecture induced by coronavirus infection in lung cells.

Brooklyn plots to identify co-expression dysregulation in single cell sequencing

Altered open chromatin regions, impacting gene expression, is a feature of some human disorders. We discovered it is possible to detect global changes in genomically-related adjacent gene co-expression within single cell RNA sequencing (scRNA-seq) data. We built a software package to generate and test non-randomness using 'Brooklyn plots' to identify the percent of genes significantly co-expressed from the same chromosome in ∼10 MB intervals across the genome. These plots establish an expected low baseline of co-expression in scRNA-seq from most cell types, but, as seen in dilated cardiomyopathy cardiomyocytes, altered patterns of open chromatin appear. These may relate to larger regions of transcriptional bursting, observable in single cell, but not bulk datasets.

Chromosome structure modeling tools and their evaluation in bacteria

The three-dimensional (3D) structure of bacterial chromosomes is crucial for understanding chromosome function. With the growing availability of high-throughput chromosome conformation capture (3C/Hi-C) data, the 3D structure reconstruction algorithms have become powerful tools to study bacterial chromosome structure and function. It is highly desired to have a recommendation on the chromosome structure reconstruction tools to facilitate the prokaryotic 3D genomics. In this work, we review existing chromosome 3D structure reconstruction algorithms and classify them based on their underlying computational models into two categories: constraint-based modeling and thermodynamics-based modeling. We briefly compare these algorithms utilizing 3C/Hi-C datasets and fluorescence microscopy data obtained from Escherichia coli and Caulobacter crescentus, as well as simulated datasets. We discuss current challenges in the 3D reconstruction algorithms for bacterial chromosomes, primarily focusing on software usability. Finally, we briefly prospect future research directions for bacterial chromosome structure reconstruction algorithms.

Correlative single molecule lattice light sheet imaging reveals the dynamic relationship between nucleosomes and the local chromatin environment

In the nucleus, biological processes are driven by proteins that diffuse through and bind to a meshwork of nucleic acid polymers. To better understand this interplay, we developed an imaging platform to simultaneously visualize single protein dynamics together with the local chromatin environment in live cells. Together with super-resolution imaging, new fluorescent probes, and biophysical modeling, we demonstrated that nucleosomes display differential diffusion and packing arrangements as chromatin density increases whereas the viscoelastic properties and accessibility of the interchromatin space remain constant. Perturbing nuclear functions impacted nucleosome diffusive properties in a manner that was dependent on local chromatin density and supportive of a model wherein transcription locally stabilizes nucleosomes while simultaneously allowing for the free exchange of nuclear proteins. Our results reveal that nuclear heterogeneity arises from both active and passive process and highlights the need to account for different organizational principals when modeling different chromatin environments.

Structure and dynamics of chemically active ring polymers: swelling to collapse

The ring structures are common in many synthetic or natural systems and experience both local and long-range forces by chemical sensing. This work is an effort to investigate the structural and dynamical properties of a chemically active ring in an explicit solvent bath utilizing hybrid molecular dynamics (MD) and multiparticle collision dynamics (MPCD) simulation techniques. We show that by tuning the chemical properties of the ring, it can be converted from a chemo-attractant to a chemo-repellent, thereby changing the steady state to be either collapsed or swelled as compared to its passive limit. We quantify these observations by comparing the scaling laws, local structures and the dynamics of active and passive rings. Furthermore, we show the impact of varying numbers of active sites by calculating the contact probability of the collapse state that highlights diverse structures. We also analyze the dynamics of the ring by finding the relaxation time and the mean square displacement of the centre of mass. A faster relaxation with enhanced diffusion is observed for the active rings.

Crumpled polymer with loops recapitulates key features of chromosome organization

Chromosomes are exceedingly long topologically-constrained polymers compacted in a cell nucleus. We recently suggested that chromosomes are organized into loops by an active process of loop extrusion. Yet loops remain elusive to direct observations in living cells; detection and characterization of myriads of such loops is a major challenge. The lack of a tractable physical model of a polymer folded into loops limits our ability to interpret experimental data and detect loops. Here, we introduce a new physical model - a polymer folded into a sequence of loops, and solve it analytically. Our model and a simple geometrical argument show how loops affect statistics of contacts in a polymer across different scales, explaining universally observed shapes of the contact probability. Moreover, we reveal that folding into loops reduces the density of topological entanglements, a novel phenomenon we refer as "the dilution of entanglements". Supported by simulations this finding suggests that up to ~ 1 - 2Mb chromosomes with loops are not topologically constrained, yet become crumpled at larger scales. Our theoretical framework allows inference of loop characteristics, draws a new picture of chromosome organization, and shows how folding into loops affects topological properties of crumpled polymers.

Theory of chromatin organization maintained by active loop extrusion

The active loop extrusion hypothesis proposes that chromatin threads through the cohesin protein complex into progressively larger loops until reaching specific boundary elements. We build upon this hypothesis and develop an analytical theory for active loop extrusion which predicts that loop formation probability is a nonmonotonic function of loop length and describes chromatin contact probabilities. We validate our model with Monte Carlo and hybrid Molecular Dynamics-Monte Carlo simulations and demonstrate that our theory recapitulates experimental chromatin conformation capture data. Our results support active loop extrusion as a mechanism for chromatin organization and provide an analytical description of chromatin organization that may be used to specifically modify chromatin contact probabilities.

Modeling of ionizing radiation-induced chromosome aberration and tumor prevalence based on two classes of DNA double-strand breaks clustering in chromatin domains

There has been some controversy over the use of radiobiological models when modeling the dose-response curves of ionizing radiation (IR)-induced chromosome aberration and tumor prevalence, as those curves usually show obvious non-targeted effects (NTEs) at low doses of high linear energy transfer (LET) radiation. The lack of understanding the contribution of NTEs to IR-induced carcinogenesis can lead to distinct deviations of relative biological effectiveness (RBE) estimations of carcinogenic potential, which are widely used in radiation risk assessment and radiation protection. In this work, based on the initial pattern of two classes of IR-induced DNA double-strand breaks (DSBs) clustering in chromatin domains and the subsequent incorrect repair processes, we proposed a novel radiobiological model to describe the dose-response curves of two carcinogenic-related endpoints within the same theoretical framework. The representative experimental data was used to verify the consistency and validity of the present model. The fitting results indicated that, compared with targeted effect (TE) and NTE models, the current model has better fitting ability when dealing with the experimental data of chromosome aberration and tumor prevalence induced by multiple types of IR with different LETs. Notably, the present model without introducing an NTE term was adequate to describe the dose-response curves of IR-induced chromosome aberration and tumor prevalence with NTEs in low-dose regions. Based on the fitting parameters, the LET-dependent RBE values were calculated for three given low doses. Our results showed that the RBE values predicted by the current model gradually decrease with the increase of doses for the endpoints of chromosome aberration and tumor prevalence. In addition, the calculated RBE was also compared with those evaluated from other models. These analyses show that the proposed model can be used as an alternative tool to well describe dose-response curves of multiple carcinogenic-related endpoints and effectively estimate RBE in low-dose regions.

Nucleus size and its effect on nucleosome stability in living cells

DNA architectural proteins play a major role in organization of chromosomal DNA in living cells by packaging it into chromatin, whose spatial conformation is determined by an intricate interplay between the DNA-binding properties of architectural proteins and physical constraints applied to the DNA by a tight nuclear space. Yet, the exact effects of the nucleus size on DNA-protein interactions and chromatin structure currently remain obscure. Furthermore, there is even no clear understanding of molecular mechanisms responsible for the nucleus size regulation in living cells. To find answers to these questions, we developed a general theoretical framework based on a combination of polymer field theory and transfer-matrix calculations, which showed that the nucleus size is mainly determined by the difference between the surface tensions of the nuclear envelope and the endoplasmic reticulum membrane as well as the osmotic pressure exerted by cytosolic macromolecules on the nucleus. In addition, the model demonstrated that the cell nucleus functions as a piezoelectric element, changing its electrostatic potential in a size-dependent manner. This effect has been found to have a profound impact on stability of nucleosomes, revealing a previously unknown link between the nucleus size and chromatin structure. Overall, our study provides new insights into the molecular mechanisms responsible for regulation of the nucleus size, as well as the potential role of nuclear organization in shaping the cell response to environmental cues.

Lattice simulation-based diffusion modelling of 3D chromatin structure

Eukaryotic nuclear genome is extensively folded in the nuclei, and the chromatin structure experiences dramatic changes, i.e., condensation and decondensation, during the cell cycle. However, a model to persuasively explain the preserved chromatin interactions during cell cycle remains lacking. In this paper, we developed two simple, lattice-based models that mimic polymer fiber decondensation from initial fractal or anisotropic condensed status, using Markov Chain Monte Carlo (MCMC) methods. By simulating the dynamic decondensation process, we observed about 8.17% and 2.03% of the interactions preserved in the condensation to decondensation transition, in the fractal diffusion and anisotropic diffusion models, respectively. Intriguingly, although interaction hubs, as a physical locus where a certain number of monomers inter-connected, were observed in diffused polymer models in both simulations, they were not associated with the preserved interactions. Our simulation demonstrated that there might exist a small portion of chromatin interactions that preserved during the diffusion process of polymers, while the interacted hubs were more dynamically formed and additional regulatory factors were needed for their preservation.

Impact of DNA Repair Kinetics and Dose Rate on RBE Predictions in the UNIVERSE

Accurate knowledge of the relative biological effectiveness (RBE) and its dependencies is crucial to support modern ion beam therapy and its further development. However, the influence of different dose rates of the reference radiation and ion beam are rarely considered. The ion beam RBE-model within our "UNIfied and VERSatile bio response Engine" (UNIVERSE) is extended by including DNA damage repair kinetics to investigate the impact of dose-rate effects on the predicted RBE. It was found that dose-rate effects increase with dose and biological effects saturate at high dose-rates, which is consistent with data- and model-based studies in the literature. In a comparison with RBE measurements from a high dose in-vivo study, the predictions of the presented modification were found to be improved in comparison to the previous version of UNIVERSE and existing clinical approaches that disregard dose-rate effects. Consequently, DNA repair kinetics and the different dose rates applied by the reference and ion beams might need to be considered in biophysical models to accurately predict the RBE. Additionally, this study marks an important step in the further development of UNIVERSE, extending its capabilities in giving theoretical guidance to support progress in ion beam therapy.

Chromosome Territories in Hematological Malignancies

Chromosomes are organized in distinct nuclear areas designated as chromosome territories (CT). The structural formation of CT is a consequence of chromatin packaging and organization that ultimately affects cell function. Chromosome positioning can identify structural signatures of genomic organization, especially for diseases where changes in gene expression contribute to a given phenotype. The study of CT in hematological diseases revealed chromosome position as an important factor for specific chromosome translocations. In this review, we highlight the history of CT theory, current knowledge on possible clinical applications of CT analysis, and the impact of CT in the development of hematological neoplasia such as multiple myeloma, leukemia, and lymphomas. Accumulating data on nuclear architecture in cancer allow one to propose the three-dimensional nuclear genomic landscape as a novel cancer biomarker for the future.

The Impact of Sub-Millisecond Damage Fixation Kinetics on the In Vitro Sparing Effect at Ultra-High Dose Rate in UNIVERSE

The impact of the exact temporal pulse structure on the potential cell and tissue sparing of ultra-high dose-rate irradiation applied in FLASH studies has gained increasing attention. A previous version of our biophysical mechanistic model (UNIVERSE: UNIfied and VERSatile bio response Engine), based on the oxygen depletion hypothesis, has been extended in this work by considering oxygen-dependent damage fixation dynamics on the sub-milliseconds scale and introducing an explicit implementation of the temporal pulse structure. The model successfully reproduces in vitro experimental data on the fast kinetics of the oxygen effect in irradiated mammalian cells. The implemented changes result in a reduction in the assumed amount of oxygen depletion. Furthermore, its increase towards conventional dose-rates is parameterized based on experimental data from the literature. A recalculation of previous benchmarks shows that the model retains its predictive power, while the assumed amount of depleted oxygen approaches measured values. The updated UNIVERSE could be used to investigate the impact of different combinations of pulse structure parameters (e.g., dose per pulse, pulse frequency, number of pulses, etc.), thereby aiding the optimization of potential clinical application and the development of suitable accelerators.

How Genomes Emerge, Function, and Evolve: Living Systems Emergence-Genotype-Phenotype-Multilism-Genome/Systems Ecology

What holds together the world in its innermost, what life is, how it emerges, functions, and evolves, has not only been an epic matter of endless romantic sunset poetry and philosophy, but also manifests explicitly in its perhaps most central organization unit-genomes. Their 3D architecture and dynamics, including the interaction networks of regulatory elements, obviously co-evolved as inseparable systems allowing the physical storage, expression, and replication of genetic information. Since we were able to fill finally the much-debated centennial gaps in their 3D architecture and dynamics, now entire new perspectives open beyond epigenetics reaching as far as a general understanding of living systems: besides the previously known DNA double helix and nucleosome structure, the latter compact into a chromatin quasi-fibre folded into stable loops forming stable multi-loop aggregates/rosettes connected by linkers, creating hence the again already known chromosome arms and entire chromosomes forming the cell nucleus. Instantly and for the first time this leads now to a consistent and cross-proven systems statistical mechanics genomics framework elucidating genome intrinsic function and regulation including various components. It balances stability/flexibility ensuring genome integrity, enabling expression/regulation of genetic information, as well as genome replication/spread. Furthermore, genotype and phenotype are multiplisticly entangled being evolutionarily the outcome of both Darwinian natural selection and Lamarckian self-referenced manipulation-all embedded in even broader genome ecology (autopoietic) i(!)n- and environmental scopes. This allows formulating new meta-level functional semantics of genomics, i.e. notions as communication of genes, genomes, and information networks, architectural and dynamic spaces for creativity and innovation, or genomes as central geno-/phenotype entanglements. Beyond and most fundamentally, the paradoxical-seeming local equilibrium substance stability in its entity though far from a universal heat-death-like equilibrium is solved, and system irreversibility, time directionality, and thus the emergence of existence are clarified. Consequently, real deep understandings of genomes, life, and complex systems in general appear in evolutionary perspectives as well as from systems analyses, via system damage/disease (its repair/cure and manipulation) as far as the understanding of extraterrestrial life, the de novo creation and thus artificial life, and even the raison d'etre.

Simulation of Different Three-Dimensional Models of Whole Interphase Nuclei Compared to Experiments - A Consistent Scale-Bridging Simulation Framework for Genome Organization

The three-dimensional architecture of chromosomes, their arrangement, and dynamics within cell nuclei are still subject of debate. Obviously, the function of genomes-the storage, replication, and transcription of genetic information-has closely coevolved with this architecture and its dynamics, and hence are closely connected. In this work a scale-bridging framework investigates how of the 30 nm chromatin fibre organizes into chromosomes including their arrangement and morphology in the simulation of whole nuclei. Therefore, mainly two different topologies were simulated with corresponding parameter variations and comparing them to experiments: The Multi-Loop-Subcompartment (MLS) model, in which (stable) small loops form (stable) rosettes, connected by chromatin linkers, and the Random-Walk/Giant-Loop (RW/GL) model, in which large loops are attached to a flexible non-protein backbone, were simulated for various loop and linker sizes. The 30 nm chromatin fibre was modelled as a polymer chain with stretching, bending and excluded volume interactions. A spherical boundary potential simulated the confinement to nuclei with different radii. Simulated annealing and Brownian Dynamics methods were applied in a four-step decondensation procedure to generate from metaphase decondensated interphase configurations at thermodynamical equilibrium. Both the MLS and the RW/GL models form chromosome territories, with different morphologies: The MLS rosettes result in distinct subchromosomal domains visible in electron and confocal laser scanning microscopic images. In contrast, the big RW/GL loops lead to a mostly homogeneous chromatin distribution. Even small changes of the model parameters induced significant rearrangements of the chromatin morphology. The low overlap of chromosomes, arms, and subchromosomal domains observed in experiments agrees only with the MLS model. The chromatin density distribution in CLSM image stacks reveals a bimodal behaviour in agreement with recent experiments. Combination of these results with a variety of (spatial distance) measurements favour an MLS like model with loops and linkers of 63 to 126 kbp. The predicted large spaces between the chromatin fibres allow typically sized biological molecules to reach nearly every location in the nucleus by moderately obstructed diffusion and is in disagreement with the much simplified assumption that defined channels between territories for molecular transport as in the Interchromosomal Domain (ICD) hypothesis exist and are necessary for transport. All this is also in agreement with recent selective high-resolution chromosome interaction capture (T2C) experiments, the scaling behaviour of the DNA sequence, the dynamics of the chromatin fibre, the diffusion of molecules, and other measurements. Also all other chromosome topologies can in principle be excluded. In summary, polymer simulations of whole nuclei compared to experimental data not only clearly favour only a stable loop aggregate/rosette like genome architecture whose local topology is tightly connected to the global morphology and dynamics of the cell nucleus and hence can be used for understanding genome organization also in respect to diagnosis and treatment. This is in agreement with and also leads to a general novel framework of genome emergence, function, and evolution.

The Physical Behavior of Interphase Chromosomes: Polymer Theory and Coarse-Grain Computer Simulations

Fluorescence in situ hybridization and chromosome conformation capture methods point to the same conclusion: that chromosomes appear to the external observer as compact structures with a highly nonrandom three-dimensional organization. In this work, we recapitulate the efforts made by us and other groups to rationalize this behavior in terms of the mathematical language and tools of polymer physics. After a brief introduction dedicated to some crucial experiments dissecting the structure of interphase chromosomes, we discuss at a nonspecialistic level some fundamental aspects of theoretical and numerical polymer physics. Then, we inglobe biological and polymer aspects into a polymer model for interphase chromosomes which moves from the observation that mutual topological constraints, such as those typically present between polymer chains in ordinary melts, induce slow chain dynamics and "constraint" chromosomes to resemble double-folded randomly branched polymer conformations. By explicitly turning these ideas into a multi-scale numerical algorithm which is described here in full details, we can design accurate model polymer conformations for interphase chromosomes and offer them for systematic comparison to experiments. The review is concluded by discussing the limitations of our approach and pointing to promising perspectives for future work.

Combined DNA Damage Repair Interference and Ion Beam Therapy: Development, Benchmark, and Clinical Implications of a Mechanistic Biological Model

PURPOSE

Our purpose was to develop a mechanistic model that describes and predicts radiation response after combined DNA damage repair interference (DDRi) and particle radiation therapy.

METHODS AND MATERIALS

The heterogeneous dose distributions of protons and ⁴He ions were implemented into the "UNIfied and VERSatile bio-response Engine" (UNIVERSE). Predictions for monoenergetic and mixed fields over clinically relevant dose and linear energy transfer range were compared with experimental in vitro survival data measured in this work as well as data available in the literature, including different cell lines and DDR interferences. Ultimately, UNIVERSE predictions were investigated in a patient plan.

RESULTS

UNIVERSE accurately predicts survival of cell lines with and without DDRi in clinical settings of ion beam therapy based only on 3 parameters derived from photon data. With increasing dose or linear energy transfer, the radiosensitizing effect of DDRi decreases, resulting in diminished relative biological effect of ion beam radiation for cells subjected to DDRi in comparison to cells that are not. Similar trends were observed in patient plan recalculations; however, this analysis also suggests that DDRi + particle radiation therapy may better preserve the therapeutic window in comparison to DDRi + photon radiation therapy.

CONCLUSIONS

The presented framework represents the first mechanistic model of combined DDRi and particle radiation therapy comprehensively benchmarked in clinically relevant scenarios and a step toward more personalized treatment. It reveals potential differences between DDRi + photon radiation therapy versus DDRi + particle radiation therapy, which have not been described so far. UNIVERSE could aid in appraising the clinical viability of combined administration of radiosensitizing drugs and charged particle therapy, as well as the identification of patients with known DDR deficiencies in the tumor who might benefit from therapy with light ions, freeing limited space at heavy ion therapy centers.

Multiscale modeling of genome organization with maximum entropy optimization

Three-dimensional (3D) organization of the human genome plays an essential role in all DNA-templated processes, including gene transcription, gene regulation, and DNA replication. Computational modeling can be an effective way of building high-resolution genome structures and improving our understanding of these molecular processes. However, it faces significant challenges as the human genome consists of over 6 × 109 base pairs, a system size that exceeds the capacity of traditional modeling approaches. In this perspective, we review the progress that has been made in modeling the human genome. Coarse-grained models parameterized to reproduce experimental data via the maximum entropy optimization algorithm serve as effective means to study genome organization at various length scales. They have provided insight into the principles of whole-genome organization and enabled de novo predictions of chromosome structures from epigenetic modifications. Applications of these models at a near-atomistic resolution further revealed physicochemical interactions that drive the phase separation of disordered proteins and dictate chromatin stability in situ. We conclude with an outlook on the opportunities and challenges in studying chromosome dynamics.

Data-Driven Polymer Model for Mechanistic Exploration of Diploid Genome Organization

Chromosomes are positioned nonrandomly inside the nucleus to coordinate with their transcriptional activity. The molecular mechanisms that dictate the global genome organization and the nuclear localization of individual chromosomes are not fully understood. We introduce a polymer model to study the organization of the diploid human genome. It is data-driven because all parameters can be derived from Hi-C data; it is also a mechanistic model because the energy function is explicitly written out based on a few biologically motivated hypotheses. These two features distinguish the model from existing approaches and make it useful both for reconstructing genome structures and for exploring the principles of genome organization. We carried out extensive validations to show that simulated genome structures reproduce a wide variety of experimental measurements, including chromosome radial positions and spatial distances between homologous pairs. Detailed mechanistic investigations support the importance of both specific interchromosomal interactions and centromere clustering for chromosome positioning. We anticipate the polymer model, when combined with Hi-C experiments, to be a powerful tool for investigating large-scale rearrangements in genome structure upon cell differentiation and tumor progression.

Modeling Direct and Indirect Action on Cell Survival After Photon Irradiation under Normoxia and Hypoxia

The demand for personalized medicine in radiotherapy has been met by a surge of mechanistic models offering predictions of the biological effect of ionizing radiation under consideration of a growing number of parameters. We present an extension of our existing model of cell survival after photon irradiation to explicitly differentiate between the damage inflicted by the direct and indirect (radicals-mediated) action of ionizing radiation. Within our approach, we assume that the oxygenation status affects the indirect action. The effect of different concentrations of dimethyl sulfoxide (DMSO), an effective radical scavenger, has been simulated at different dose levels in normoxic and hypoxic conditions for various cell lines. Our model is found to accurately predict experimental data available in literature, validating the assumptions made in our approach. The presented extension adds further flexibility to our model and could act as basis for further developments of our model.

Physical and data structure of 3D genome

With the textbook view of chromatin folding based on the 30-nm fiber being challenged, it has been proposed that interphase DNA has an irregular 10-nm nucleosome polymer structure whose folding philosophy is unknown. Nevertheless, experimental advances suggest that this irregular packing is associated with many nontrivial physical properties that are puzzling from a polymer physics point of view. Here, we show that the reconciliation of these exotic properties necessitates modularizing three-dimensional genome into tree data structures on top of, and in striking contrast to, the linear topology of DNA double helix. These functional modules need to be connected and isolated by an open backbone that results in porous and heterogeneous packing in a quasi-self-similar manner, as revealed by our electron and optical imaging. Our multiscale theoretical and experimental results suggest the existence of higher-order universal folding principles for a disordered chromatin fiber to avoid entanglement and fulfill its biological functions.

Modeling the Effect of Hypoxia and DNA Repair Inhibition on Cell Survival After Photon Irradiation

Mechanistic approaches to modeling the effects of ionizing radiation on cells are on the rise, promising a better understanding of predictions and higher flexibility concerning conditions to be accounted for. In this work we modified and extended a previously published mechanistic model of cell survival after photon irradiation under hypoxia to account for radiosensitization caused by deficiency or inhibition of DNA damage repair enzymes. The model is shown to be capable of describing the survival data of cells with DNA damage repair deficiency, both under norm- and hypoxia. We find that our parameterization of radiosensitization is invariant under change of oxygen status, indicating that the relevant parameters for both mechanisms can be obtained independently and introduced freely to the model to predict their combined effect.

The Rabl configuration limits topological entanglement of chromosomes in budding yeast

The three dimensional organization of genomes remains mostly unknown due to their high degree of condensation. Biophysical studies predict that condensation promotes the topological entanglement of chromatin fibers and the inhibition of function. How organisms balance between functionally active genomes and a high degree of condensation remains to be determined. Here we hypothesize that the Rabl configuration, characterized by the attachment of centromeres and telomeres to the nuclear envelope, helps to reduce the topological entanglement of chromosomes. To test this hypothesis we developed a novel method to quantify chromosome entanglement complexity in 3D reconstructions obtained from Chromosome Conformation Capture (CCC) data. Applying this method to published data of the yeast genome, we show that computational models implementing the attachment of telomeres or centromeres alone are not sufficient to obtain the reduced entanglement complexity observed in 3D reconstructions. It is only when the centromeres and telomeres are attached to the nuclear envelope (i.e. the Rabl configuration) that the complexity of entanglement of the genome is comparable to that of the 3D reconstructions. We therefore suggest that the Rabl configuration is an essential player in the simplification of the entanglement of chromatin fibers.

Chromosome territories and the global regulation of the genome

Spatial positioning is a fundamental principle governing nuclear processes. Chromatin is organized as a hierarchy from nucleosomes to Mbp chromatin domains (CD) or topologically associating domains (TADs) to higher level compartments culminating in chromosome territories (CT). Microscopic and sequencing techniques have substantiated chromatin organization as a critical factor regulating gene expression. For example, enhancers loop back to interact with their target genes almost exclusively within TADs, distally located coregulated genes reposition into common transcription factories upon activation, and Mbp CDs exhibit dynamic motion and configurational changes in vivo. A longstanding question in the nucleus field is whether an interactive nuclear matrix provides a direct link between structure and function. The findings of nonrandom radial positioning of CT within the nucleus suggest the possibility of preferential interaction patterns among populations of CT. Sequential labeling up to 10 CT followed by application of computer imaging and geometric graph mining algorithms revealed cell-type specific interchromosomal networks (ICN) of CT that are altered during the cell cycle, differentiation, and cancer progression. It is proposed that the ICN correlate with the global level of genome regulation. These approaches also demonstrated that the large scale 3-D topology of CT is specific for each CT. The cell-type specific proximity of certain chromosomal regions in normal cells may explain the propensity of distinct translocations in cancer subtypes. Understanding how genes are dysregulated upon disruption of the normal "wiring" of the nucleus by translocations, deletions, and amplifications that are hallmarks of cancer, should enable more targeted therapeutic strategies.

Leukocyte Nucleus Reveals a Linear Order of Chromosomes Separated in Two Parental Genomes That Favors the Process of Gene Activation

Analysis of trisomy 8 cells and the chromosome-specific fluorescence in situ hybridization (FISH) signals on the ring-shaped nucleus of a neutrophil reveal that homologue chromosomes orient in diametrical opposition to each other. This positioning results in a separation of the two haploid sets of parental chromosomes organized as two exclusive groups. These two groups impart the nucleus a symmetry that fortifies immune protection by accelerating chemotaxis. The ring form of the nucleus is a legacy of the orientation of chromosomes as a rosette during metaphase and telophase stages. A dual control maintains this spatial order: (1) chromosomes are tethered to the centriole all through the cell cycle, and (2) during their circular orientation in telophase the chromosomes bind to each other with lamins, which reorganize the nuclear membrane of the daughter nuclei, generating an additional anchorage. Here, chromosomes serve as temporary packets to assure proper distribution of the nuclear DNA during mitosis. The remainder time of the cell cycle the chromosomes are chained together across the telomeres, allowing a continuous sequence of genes of the two genomes, maternal and paternal, thus facilitating easy reading of the gene sequence. Exceptions to these orders are either physiological and temporary, or pathological and disease causing.

Genomic 3D compartments emerge from unfolding mitotic chromosomes

The 3D organisation of the genome in interphase cells is not a randomly folded polymer. Rather, experiments show that chromosomes arrange into a network of 3D compartments that correlate with biological processes, such as transcription, chromatin modifications and protein binding. However, these compartments do not exist during cell division when the DNA is condensed, and it is unclear how and when they emerge. In this paper, we focus on the early stages after cell division as the chromosomes start to decondense. We use a simple polymer model to understand the types of 3D structures that emerge from local unfolding of a compact initial state. From simulations, we recover 3D compartments, such as TADs and A/B compartments that are consistently detected in chromosome capture experiments across cell types and organisms. This suggests that the large-scale 3D organisation is a result of an inflation process.

A Guided Protocol for Array Based T2C: A High-Quality Selective High-Resolution High-Throughput Chromosome Interaction Capture

After now more than 170 years of research the dynamic three-dimensional chromatin architecture of genomes and the co-evolved interaction networks of regulatory elements which create genome function - i.e. the storage, expression, and finally replication of genetic information - involves ever more investigative efforts in respect to not only the pure understanding of living organisms, but also diagnosis, treatment, and even future genome engineering. To study genomic interactions, we developed a novel and superior high-quality selective high-resolution, high-throughput chromosome interaction capture method - T2C (targeted chromatin capture) - which allows to arbitrarily balance resolution, frequency range of interactions, and the investigated general genetic region or single interactions in a highly cost-effective manner in respect to the obtainable result and compared to other techniques. Beyond, T2C has such a high signal-to-noise ratio at high resolution that the "genomic" statistical mechanics level can be reached. With the guided T2C protocol described here, we were already able to finally determine the chromatin quasi-fiber conformation and its folding into stable multi-loop aggregates/rosettes connected by a linker. Actually, this guided T2C protocol provides the means for architectural genome sequencing from the level of the single base pair to the entire cell nucleus and thus to analyze genetic interactions in respect to genome function in a systems biological manner in general as well as in settings ranging from basic research, via diagnostics and treatment, to genome engineering. © 2018 by John Wiley & Sons, Inc.

Simulation of different three-dimensional polymer models of interphase chromosomes compared to experiments-an evaluation and review framework of the 3D genome organization

Despite all the efforts the three-dimensional higher-order architecture and dynamics in the cell nucleus are still debated. The regulation of genes, their transcription, replication, as well as differentiation in Eukarya is, however, closely connected to this architecture and dynamics. Here, an evaluation and review framework is setup to investigate the folding of a 30 nm chromatin fibre into chromosome territories by comparing computer simulations of two different chromatin topologies to experiments: The Multi-Loop-Subcompartment (MLS) model, in which small loops form rosettes connected by chromatin linkers, and the Random-Walk/Giant-Loop (RW/GL) model, in which large loops are attached to a flexible non-protein backbone, were simulated for various loop, rosette, and linker sizes. The 30 nm chromatin fibre was modelled as a polymer chain with stretching, bending, and excluded volume interactions. A spherical boundary potential simulated the confinement by other chromosomes and the nuclear envelope. Monte Carlo and Brownian Dynamics methods were applied to generate chain configurations at thermodynamic equilibrium. Both the MLS and the RW/GL models form chromosome territories, with different morphologies: The MLS rosettes form distinct subchromosomal domains, compatible in size as those from light microscopic observations. In contrast, the big RW/GL loops lead to a more homogeneous chromatin distribution. Only the MLS model agrees with the low overlap of chromosomes, their arms, and subchromosomal domains found experimentally. A review of experimental spatial distance measurements between genomic markers labelled by FISH as a function of their genomic separation from different publications and comparison to simulated spatial distances also favours an MLS-like model with loops and linkers of 63 to 126 kbp. The chromatin folding topology also reduces the apparent persistence length of the chromatin fibre to a value significantly lower than the free solution persistence length, explaining the low persistence lengths found various experiments. The predicted large spaces between the chromatin fibres allow typically sized biological molecules to reach nearly every location in the nucleus by moderately obstructed diffusion and disagrees with the much simplified assumption that defined channels between territories for molecular transport as in the Interchromosomal Domain (ICD) hypothesis exist. All this is also in agreement with recent selective high-resolution chromosome interaction capture (T2C) experiments, the scaling behaviour of the DNA sequence, the dynamics of the chromatin fibre, the nuclear diffusion of molecules, as well as other experiments. In summary, this polymer simulation framework compared to experimental data clearly favours only a quasi-chromatin fibre forming a stable multi-loop aggregate/rosette like genome organization and dynamics whose local topology is tightly connected to the global morphology and dynamics of the cell nucleus.

Interphase human chromosome exhibits out of equilibrium glassy dynamics

Fingerprints of the three-dimensional organization of genomes have emerged using advances in Hi-C and imaging techniques. However, genome dynamics is poorly understood. Here, we create the chromosome copolymer model (CCM) by representing chromosomes as a copolymer with two epigenetic loci types corresponding to euchromatin and heterochromatin. Using novel clustering techniques, we establish quantitatively that the simulated contact maps and topologically associating domains (TADs) for chromosomes 5 and 10 and those inferred from Hi-C experiments are in good agreement. Chromatin exhibits glassy dynamics with coherent motion on micron scale. The broad distribution of the diffusion exponents of the individual loci, which quantitatively agrees with experiments, is suggestive of highly heterogeneous dynamics. This is reflected in the cell-to-cell variations in the contact maps. Chromosome organization is hierarchical, involving the formation of chromosome droplets (CDs) on genomic scale, coinciding with the TAD size, followed by coalescence of the CDs, reminiscent of Ostwald ripening.

The biology and polymer physics underlying large-scale chromosome organization

Chromosome large-scale organization is a beautiful example of the interplay between physics and biology. DNA molecules are polymers and thus belong to the class of molecules for which physicists have developed models and formulated testable hypotheses to understand their arrangement and dynamic properties in solution, based on the principles of polymer physics. Biologists documented and discovered the biochemical basis for the structure, function and dynamic spatial organization of chromosomes in cells. The underlying principles of chromosome organization have recently been revealed in unprecedented detail using high-resolution chromosome capture technology that can simultaneously detect chromosome contact sites throughout the genome. These independent lines of investigation have now converged on a model in which DNA loops, generated by the loop extrusion mechanism, are the basic organizational and functional units of the chromosome.

Role of special cross-links in structure formation of bacterial DNA polymer

Using data from contact maps of the DNA-polymer of Escherichia coli (E. Coli) (at kilobase pair resolution) as an input to our model, we introduce cross-links between monomers in a bead-spring model of a ring polymer at very specific points along the chain. Via suitable Monte Carlo simulations, we show that the presence of these cross-links leads to a particular organization of the chain at large (micron) length scales of the DNA. We also investigate the structure of a ring polymer with an equal number of cross-links at random positions along the chain. We find that though the polymer does get organized at the large length scales, the nature of the organization is quite different from the organization observed with cross-links at specific biologically determined positions. We used the contact map of E. Coli bacteria which has around 4.6 million base pairs in a single circular chromosome. In our coarse-grained flexible ring polymer model, we used 4642 monomer beads and observed that around 80 cross-links are enough to induce the large-scale organization of the molecule accounting for statistical fluctuations caused by thermal energy. The length of a DNA chain even of a simple bacterial cell such as E. Coli is much longer than typical proteins, hence we avoided methods used to tackle protein folding problems. We define new suitable quantities to identify the large scale structure of a polymer chain with a few cross-links.

The 10-nm chromatin fiber and its relationship to interphase chromosome organization

A chromosome is a single long DNA molecule assembled along its length with nucleosomes and proteins. During interphase, a mammalian chromosome exists as a highly organized supramolecular globule in the nucleus. Here, we discuss new insights into how genomic DNA is packaged and organized within interphase chromosomes. Our emphasis is on the structural principles that underlie chromosome organization, with a particular focus on the intrinsic contributions of the 10-nm chromatin fiber, but not the regular 30-nm fiber. We hypothesize that the hierarchical globular organization of an interphase chromosome is fundamentally established by the self-interacting properties of a 10-nm zig-zag array of nucleosomes, while histone post-translational modifications, histone variants, and chromatin-associated proteins serve to mold generic chromatin domains into specific structural and functional entities.

Two loci single particle trajectories analysis: constructing a first passage time statistics of local chromatin exploration

Stochastic single particle trajectories are used to explore the local chromatin organization. We present here a statistical analysis of the first contact time distributions between two tagged loci recorded experimentally. First, we extract the association and dissociation times from data for various genomic distances between loci, and we show that the looping time occurs in confined nanometer regions. Second, we characterize the looping time distribution for two loci in the presence of multiple DNA damages. Finally, we construct a polymer model, that accounts for the local chromatin organization before and after a double-stranded DNA break (DSB), to estimate the level of chromatin decompaction. This novel passage time statistics method allows extracting transient dynamic at scales varying from one to few hundreds of nanometers, it predicts the local changes in the number of binding molecules following DSB and can be used to characterize the local dynamic of the chromatin.

FISH-ing for captured contacts: towards reconciling FISH and 3C

Chromosome conformation capture (3C) and fluorescence in situ hybridization (FISH) are two widely used technologies that provide distinct readouts of 3D chromosome organization. While both technologies can assay locus-specific organization, how to integrate views from 3C, or genome-wide Hi-C, and FISH is far from solved. Contact frequency, measured by Hi-C, and spatial distance, measured by FISH, are often assumed to quantify the same phenomena and used interchangeably. Here, however, we demonstrate that contact frequency is distinct from average spatial distance, both in polymer simulations and in experimental data. Performing a systematic analysis of the technologies, we show that this distinction can create a seemingly paradoxical relationship between 3C and FISH, both in minimal polymer models with dynamic looping interactions and in loop-extrusion simulations. Together, our results indicate that cross-validation of Hi-C and FISH should be carefully designed, and that jointly considering contact frequency and spatial distance is crucial for fully understanding chromosome organization.

Transient chromatin properties revealed by polymer models and stochastic simulations constructed from Chromosomal Capture data

Chromatin organization can be probed by Chromosomal Capture (5C) data, from which the encounter probability (EP) between genomic sites is presented in a large matrix. This matrix is averaged over a large cell population, revealing diagonal blocks called Topological Associating Domains (TADs) that represent a sub-chromatin organization. To study the relation between chromatin organization and gene regulation, we introduce a computational procedure to construct a bead-spring polymer model based on the EP matrix. The model permits exploring transient properties constrained by the statistics of the 5C data. To construct the polymer model, we proceed in two steps: first, we introduce a minimal number of random connectors inside restricted regions to account for diagonal blocks. Second, we account for long-range frequent specific genomic interactions. Using the constructed polymer, we compute the first encounter time distribution and the conditional probability of three key genomic sites. By simulating single particle trajectories of loci located on the constructed polymers from 5C data, we found a large variability of the anomalous exponent, used to interpret live cell imaging trajectories. The present polymer construction provides a generic tool to study steady-state and transient properties of chromatin constrained by some physical properties embedded in 5C data.

Chromatin organization remains poorly understood and polymer models are used to reconstruct such organization, to reveal hidden structures and to quantify genomic interactions. We use a generalized Rouse model (a linear chain of beads connected by springs) with additional interacting molecules that allow stable loop formation. The polymer models are constructed using the minimal number of binding molecules, positioned according to the encounter probability matrix obtained from experimental chromosomal capture data. We determine the conditional encounter probability of 3 key loci regulating gene inactivation from our calibrated polymer model. Using polymer simulations, we generate single particle trajectories and explore their transient properties. The present results suggest that the heterogeneity of anomalous exponents measured in live cell imaging is due to the large combinatorics in reconstructing the chromatin organization from Chromosomal Capture data. The present method and algorithms are generic and can be used to reconstruct a polymer model at a given scale from any Chromosomal Capture data.

How does chromatin package DNA within nucleus and regulate gene expression?

The human body is made up of 60 trillion cells, each cell containing 2 millions of genomic DNA in its nucleus. How is this genomic deoxyribonucleic acid [DNA] organised into nuclei? Around 1880, W. Flemming discovered a nuclear substance that was clearly visible on staining under primitive light microscopes and named it 'chromatin'; this is now thought to be the basic unit of genomic DNA organization. Since long before DNA was known to carry genetic information, chromatin has fascinated biologists. DNA has a negatively charged phosphate backbone that produces electrostatic repulsion between adjacent DNA regions, making it difficult for DNA to fold upon itself. In this article, we will try to shed light on how does chromatin package DNA within nucleus and regulate gene expression?

Linking Chromatin Fibers to Gene Folding by Hierarchical Looping

While much is known about DNA structure on the basepair level, this scale represents only a fraction of the structural levels involved in folding the genomic material. With recent advances in experimental and theoretical techniques, a variety of structures have been observed on the fiber, gene, and chromosome levels of genome organization. Here we view chromatin architecture from nucleosomes and fibers to genes and chromosomes, highlighting the rich structural diversity and fiber fluidity emerging from both experimental and theoretical techniques. In this context, we discuss our recently proposed folding mechanism, which we call "hierarchical looping", similar to rope flaking used in mountain climbing, where 10-nm zigzag chromatin fibers are compacted laterally into self-associating loops which then stack and fold in space. We propose that hierarchical looping may act as a bridge between fibers and genes as well as provide a mechanism to relate key features of interphase and metaphase chromosome architecture to genome structural changes. This motif emerged by analysis of ultrastructural internucleosome contact data by electron microscopy-assisted nucleosome interaction capture cross-linking experiments, in combination with mesoscale modeling. We suggest that while the local folding of chromatin can be regulated at the fiber level by adjustment of internal factors such as linker-histone binding affinities, linker DNA lengths, and divalent ion levels, hierarchical looping on the gene level can additionally be controlled by posttranslational modifications and external factors such as polycomb group proteins. From a combination of 3C data and mesoscale modeling, we suggest that hierarchical looping could also play a role in epigenetic gene silencing, as stacked loops may occlude access to transcription start sites. With advances in crystallography, single-molecule in vitro biochemistry, in vivo imaging techniques, and genome-wide contact data experiments, various modeling approaches are allowing for previously unavailable structural interpretation of these data at multiple spatial and temporal scales. An unprecedented level of productivity and opportunity is on the horizon for the chromatin structure field.

The detailed 3D multi-loop aggregate/rosette chromatin architecture and functional dynamic organization of the human and mouse genomes

BACKGROUND

The dynamic three-dimensional chromatin architecture of genomes and its co-evolutionary connection to its function-the storage, expression, and replication of genetic information-is still one of the central issues in biology. Here, we describe the much debated 3D architecture of the human and mouse genomes from the nucleosomal to the megabase pair level by a novel approach combining selective high-throughput high-resolution chromosomal interaction capture (T2C), polymer simulations, and scaling analysis of the 3D architecture and the DNA sequence.

RESULTS

The genome is compacted into a chromatin quasi-fibre with ~5 ± 1 nucleosomes/11 nm, folded into stable ~30-100 kbp loops forming stable loop aggregates/rosettes connected by similar sized linkers. Minor but significant variations in the architecture are seen between cell types and functional states. The architecture and the DNA sequence show very similar fine-structured multi-scaling behaviour confirming their co-evolution and the above.

CONCLUSIONS

This architecture, its dynamics, and accessibility, balance stability and flexibility ensuring genome integrity and variation enabling gene expression/regulation by self-organization of (in)active units already in proximity. Our results agree with the heuristics of the field and allow "architectural sequencing" at a genome mechanics level to understand the inseparable systems genomic properties.

Dynamic properties of independent chromatin domains measured by correlation spectroscopy in living cells

Background

Genome organization into subchromosomal topologically associating domains (TADs) is linked to cell-type-specific gene expression programs. However, dynamic properties of such domains remain elusive, and it is unclear how domain plasticity modulates genomic accessibility for soluble factors.

Results

Here, we combine and compare a high-resolution topology analysis of interacting chromatin loci with fluorescence correlation spectroscopy measurements of domain dynamics in single living cells. We identify topologically and dynamically independent chromatin domains of ~1 Mb in size that are best described by a loop-cluster polymer model. Hydrodynamic relaxation times and gyration radii of domains are larger for open (161 ± 15 ms, 297 ± 9 nm) than for dense chromatin (88 ± 7 ms, 243 ± 6 nm) and increase globally upon chromatin hyperacetylation or ATP depletion.

Conclusions

Based on the domain structure and dynamics measurements, we propose a loop-cluster model for chromatin domains. It suggests that the regulation of chromatin accessibility for soluble factors displays a significantly stronger dependence on factor concentration than search processes within a static network.

Electronic supplementary material

The online version of this article (doi:10.1186/s13072-016-0093-1) contains supplementary material, which is available to authorized users.